Weighted norm inequalities for averaging operators of monotone functions.
We prove weighted norm inequalities for the averaging operator Af(x) = 1/x ∫0x f of monotone functions.
Weighted norm inequalities for parabolic fractional integrals
Weighted power mean discrete dynamical systems: fast convergence properties.
Weighted Theorems on Fractional Integrals in the Generalized Hölder Spaces via Indices mω and Mω
Mathematics Subject Classification: 26A16, 26A33, 46E15.There are known various statements on weighted action of one-dimensional and multidimensional fractional integration operators in spaces of continuous functions, such as weighted generalized Hölder spaces Hω0(ρ) of functions with a given dominant ω of their continuity modulus.
Well-Posedness of Diffusion-Wave Problem with Arbitrary Finite Number of Time Fractional Derivatives in Sobolev Spaces H^s
Mathematics Subject Classification 2010: 26A33, 33E12, 35S10, 45K05.We give the proofs of the existence and regularity of the solutions in the space C^∞ (t > 0;H^(s+2) (R^n)) ∩ C^0(t ≧ 0;H^s(R^n)); s ∊ R, for the 1-term, 2-term,..., n-term time-fractional equation evaluated from the time fractional equation of distributed order with spatial Laplace operator Δx ...
Well-Posedness of the Cauchy Problem for Inhomogeneous Time-Fractional Pseudo-Differential Equations
Mathematics Subject Classification: 26A33, 45K05, 35A05, 35S10, 35S15, 33E12In the present paper the Cauchy problem for partial inhomogeneous pseudo-differential equations of fractional order is analyzed. The solvability theorem for the Cauchy problem in the space ΨG,2(R^n) of functions in L2(R^n) whose Fourier transforms are compactly supported in a domain G ⊆ R^n is proved. The representation of the solution in terms of pseudo-differential operators is given. The solvability theorem in the Sobolev...
When finely continuous functions are of the first class of Baire
When is any continuous function Lipschitzian?
Where are typical functions one-to-one?
Suppose is closed. Is it true that the typical (in the sense of Baire category) function in is one-to-one on ? If we show that the answer to this question is yes, though we construct an with for which the answer is no. If is the middle- Cantor set we prove that the answer is yes if and only if There are ’s with Hausdorff dimension one for which the answer is still yes. Some other related results are also presented.
Whitney arcs and 1-critical arcs
A simple arc γ ⊂ ℝⁿ is called a Whitney arc if there exists a non-constant real function f on γ such that for every x ∈ γ; γ is 1-critical if there exists an f ∈ C¹(ℝⁿ) such that f’(x) = 0 for every x ∈ γ and f is not constant on γ. We show that the two notions are equivalent if γ is a quasiarc, but for general simple arcs the Whitney property is weaker. Our example also gives an arc γ in ℝ² each of whose subarcs is a monotone Whitney arc, but which is not a strictly monotone Whitney arc. This...
X-minimal patterns and a generalization of Sharkovskiĭ's theorem
We study the law of coexistence of different types of cycles for a continuous map of the interval. For this we introduce the notion of eccentricity of a pattern and characterize those patterns with a given eccentricity that are simplest from the point of view of the forcing relation. We call these patterns X-minimal. We obtain a generalization of Sharkovskiĭ's Theorem where the notion of period is replaced by the notion of eccentricity.
Základové arithmetiky. [I.]
Základy theorie integrálu v Euklidových prostorech. [I.]
Základy theorie integrálu v Euklidových prostorech. [II.]
Základy theorie integrálu v Euklidových prostorech. [III.]
Zeros of continuous functions and the structure of two function spaces
Zur Induktion im Kontinuum.
Zur konstruktiven Differenzierbarkeit von monotonen berechenbaren Funktionen.
Zur Theorie der Functionen.
Zur Übereinstimmung der Mittelwertstellen von Funktionen und ihren Ableitungen.